The Effect of Dynamic Permeability on Velocity and Intrinsic Attenuation of Compressional Waves in Sand

Document Type: Research Papers


1 Assistant Professor, K.N. Toosi University of Technology, Civil Engineering Faculty, Tehran, Iran

2 MSc Graduate, K.N. Toosi University of Technology, Civil Engineering Faculty, Tehran, Iran


Stress waves contain useful information about the properties of porous materials; they can be recovered through different non-destructive testing methods such as crosswell, vertical seismic profile, borehole logging as well as sonic tests. In all these methods, it is crucial to assess the effects of frequency on wave attributes including velocity and intrinsic attenuation. The dependency of permeability on frequency which is known as dynamic permeability and its effects on wave attributes of compressional waves are investigated in the present paper. Utilizing the dispersion relation derived for compressional waves, it is shown how the velocity and intrinsic attenuation of waves propagated in water saturated sand may be influenced by dynamic permeability. In low frequency range (viscous dominated flow regime), the dynamic permeability behaves like Darcy steady-state permeability and its effects on wave attributes are negligible. However, deviations from Darcy permeability start to occur at higher frequencies. Therefore, it is important to know how dynamic permeability controls the behavior of wave velocity and intrinsic attenuation in relatively high frequencies.  For example, it is demonstrated that neglecting dynamic permeability results in overestimation of velocities of fast and slow waves in high frequency ranges (inertia dominated flow regime).


Allard, J., Henry, M., Tizianel, J., Kelders, L. and Lauriks, W. (1998). “Sound propagation in air saturated random packings of beads”, Journal of Acoustical Society of America, 104, 2004–2007.

Berryman, J.G. (1980). “Confirmation of Biot's theory”, Applied Physics Letter, 37(4), 382-384.

Biot, M.A. (1956a). “Theory of Propagation of Elastic Waves in Fluid-Saturated Porous Solid: Low Frequency Range”, Journal of Acoustical Society of America, 28, 168–178.

Biot, M.A. (1956b). “Theory of Propagation of Elastic Waves in Fluid-Saturated Porous Solid: Higher frequency range”, Journal of Journal of Acoustical Society of America, 28, 179–191.

Chapman, A. and Higdon, J. (1992). “Oscillatory stokes flow in periodic porous media”, Physics of Fluids, 4(10), 2099–2116.

Charlaix, E., Kushnick, A. and Stokes, J. (1988). “Experimental study of dynamic permeability in porous media”, Physical Review Letters, 61, 1595–1598.

Ghasemzadeh, H. and Abounouri, A.A. (2012). “Effect of subsurface hydrological properties on velocity and attenuation of compressional and shear wave in fluid-saturated viscoelastic porous media”, Journal of Hydrology, 460–461, 110–116.

Iversen, N. and Jørgensen, B.B. (1993). “Diffusion coefficients of sulfate and methane in marine sediments: Influence of porosity”, Geochimica et Cosmochimica, 57, 571–578.

Johnson, D.L., Hemmick, D. and Kojima, H. (1994). “Probing porous media with first and second sound. i. dynamic permeability”, Journal of Applied Physics, 76, 104–114.

Johnson, D.L., Koplik, J. and Dashen, R. (1987). “Theory of Dynamic Permeability and Tortuosity in Fluid–Saturated Porous–Media”, Journal of Fluid Mechanics, 176, 379–402.

Kim, S.H., Kim, K.J. and Blouin, S.E. (2002). “Analysis of wave propagation in saturated porous media. I. Theoretical solution”, Computer Methods in Applied Mechanics and Engineering, 191, 4061–4073.

Lo, W.C., Sposito, G. and Majer, E. (2006). “Low-frequency dilatational wave propagation through fully-saturated poroelastic media”, Advances in Water Resources, 29, 408–416.

Lo, W.C., Yeh, C.L. and Jan, C.D. (2008). “Effect of soil texture and excitation frequency on the propagation and attenuation of acoustic waves at saturated conditions”, Journal of Hydrology, 357, 270–281.

Sheng, P. and Zhou, M.Y. (1988). “Dynamic permeability in porous medium”, Physical Review Letters, 61, 1591–1594.

Smeulders, D.M.J. (1992). “On Wave Propagation in Saturated and Partially Saturated Porous Media”, PhD Thesis, Eindhoven University of Technology.

Theodorakopoulos, D.D. and Beskos, D.E. (2006). “Application of Biot’s Poroelasticity to Some Soil Dynamics Problems in Civil Engineering”, Soil Dynamics and Earthquake Engineering, 26, 666–679.

Verruijt, A. (2010). An Introduction to Soil Dynamics, Springer, New York.